The capability of the standard SST k-ω turbulence model for the prediction of jet impingement cooling characteristics using a coarse mesh is investigated. The discussion is based on a sensitivity study with five computational grids, differing from each other in topology and resolution. The analysis considers a hexagonal configuration of turbulent jets at the inlet Reynolds number equal to 20,000, with the distance between the nozzle and target plates equal to four nozzle diameters. The results of steady RANS simulations are validated against the time-averaged LES results and data from experiments. The mean heat transfer characteristics of turbulent impinging jets have been successfully reproduced with all tested grids, which indicates that for a rather accurate mean heat transfer prediction, it is not necessary to resolve all the small-scale flow features of impinging jets above the target plate.
Industrial multiphase flows are typically characterized by coexisting morphologies. Modern simulation methods are well established for dispersed [e.g., Euler-Euler (E-E)] or resolved [e.g., volume-of-fluid (VOF)] interfacial structures. Hence, a morphology adaptive multifield two-fluid model is proposed that is able to handle dispersed and resolved interfacial structures coexisting in the computational domain with the same set of equations. An interfacial drag formulation for large interfacial structures is used to describe them in a VOF-like manner. For the dispersed structures, the baseline model developed at Helmholtz-Zentrum Dresden-Rossendorf is applied. The functionality of the framework is demonstrated by investigating a single rising gas bubble in a stagnant water column, a two-dimensional stagnant stratification of water and oil sharing a large-scale interface that is penetrated by micro gas bubbles, and an isothermal countercurrent stratified flow case. Recent developments focus on the transition region, where bubbles are overresolved or underresolved either for E-E or for VOF. Furthermore, a concept is presented for the transition of oversized dispersed bubbles into the resolved phase.
In two-fluid simulations of flow boiling, the modeling of the mean bubble diameter is a key parameter in the closure relations governing the intefacial transfer of mass, momentum, and energy. Monodispersed approach proved to be insufficient to describe the significant variation in bubble size during flow boiling in a heated pipe. A population balance model (PBM) has been employed to address these shortcomings. During nucleate boiling, vapor bubbles of a certain size are formed on the heated wall, detach and migrate into the bulk flow. These bubbles then grow, shrink or disintegrate by evaporation, condensation, breakage and aggregation. In this study, a parametric analysis of the PBM aggregation and breakage models has been performed to investigate their effect on the radial distribution of the mean bubble diameter and vapor volume fraction. The simulation results are compared with the DEBORA experiments (Garnier et al., 2001). In addition, the influence of PBM parameters on the local distribution of individual bubble size groups was also studied. The results have shown that the modeling of aggregation process has the largest influence on the results and is mainly dictated by the collisions due to flow turbulence.
A benchmark activity on two-fluid simulations of high-pressure boiling upward flows in a pipe is performed by 12 participants using different MCFD (Multiphase Computational Fluid Dynamics) codes and closure relationships. More than 30 conditions from DEBORA experiment conducted by CEA are considered. Each case is characterised by the flow rate, inlet temperature, wall heat flux and outlet pressure. High-pressure Freon (R12) at 14 bar and 26 bar is boiled in a 19.2mm pipe heated over 3.5m. Flow rates range from 2000 kg m−2 s−1 to 5000 kg m−2 s−1 and exit quality x ranges from single-phase conditions to x=0.1 which leads to a peak void fraction of α=70%. In these high pressure conditions, bubbles remain small and there is no departure from the bubbly flow regime (François et al., 2011; Hösler, 1968). However, different kind of bubbly flows are observed: wall-peak, intermediate peak or core-peak, depending on the case considered. Measurements along the pipe radius near the end of the heated section are compared to code predictions. They include void fraction, bubble mean diameter, vapour velocity and liquid temperature. The benchmark covered two phases. In the first phase of the benchmark activities, experimental data were given to the participants, allowing to compare the simulation results and to develop, to select or to adjust the models in the CMFD codes. The second phase included blind cases where the participants could not compare to the measurements. In between the two phases, possible additional model adjustments or calibrations were performed. Overall, the benchmark involved very different closures and a wide range of models' complexity was covered. Yet, it is extremely difficult to have a robust closure for all conditions considered, even knowing experimental measurements. The wall-to-core peak transition is not captured consistently by the models. The degree of subcooling and the void fraction level are also difficult to assess. We were not capable of showing superiority of some physical closures, even for part of the model. The interaction between mechanisms and their hierarchy are extremely difficult to understand. Although departure from nucleate boiling (DNB) was not considered in this benchmarking exercise, it is expected that DNB predictions at high-pressure conditions depend strongly on the near-wall flow, temperature, and void fraction distributions. Therefore, the suitability of the closures also limits the accuracy of DNB predictions. The benchmark also demonstrated that in order to progress further in models development and validation, it is compulsory to have new measurements that include simultaneously as many variables as possible (including liquid temperature, velocity, cross-correlations and wall temperature); also, a better knowledge of the local bubble sizes distributions is the key to discriminate performances of interfacial area modelling (IATE, MUSIG or iMUSIG models, considering for instance the possibility of two classes of bubbles having totally different behaviour regarding the lift force). Following this benchmark impulse, we hope that future activities will be engaged on high-pressure boiling water experiments with a continuation of models' comparisons and development.
The morphology-adaptive multifield two-fluid model MultiMorph focuses on the reliable and robust simulation of interfacial multiphase flows in industrial applications. The idea is to combine the Volume-of-Fluid approach with the Euler-Euler approach to model both large and small scale interfacial structures efficiently. The choice of the local representation of interfacial structures, such as bubbles or droplets, by either the first or the second of the aforementioned basic method strongly depends on the ratio of the length scale of the interface feature to the grid spacing. In case the computational grid gets too coarse to locally resolve an interfacial structure, a morphology transfer is required. Such a transfer process allows to convert resolved fluid into non-resolved one, i.e. changing from a continuous description to a disperse one. A formulation for such a numerically motivated morphology transfer process is presented. It is validated with a case of a two-dimensional single rising bubble on a grid with gradually varying cell size. The model is then applied to two further cases: an oil–water phase inversion and a water jet plunging into a free water surface. Hereby, functionality, robustness and feasibility of the proposed morphology transfer mechanism are demonstrated. This work contributes to a hybrid modelling approach for the simulation of two-phase flows adapting the numerical representation depending on local flow morphology and on available computational resources.
Modeling of annular flow with the computational fluid dynamics (CFD) is challenging as one has to consider several, rather different, phenomena simultaneously: the continuous liquid film, continuous gas core, and dispersed droplets. A morphology-adaptive multifield two-fluid model (MultiMorph) developed by Meller et al. [“Basic verification of a numerical framework applied to a morphology adaptive multifield two-fluid model considering bubble motions,” Int. J. Numer. Methods Fluids 93(3), 748–773 (2021)], with three numerical phase fields, is well suited to simulate such multiple flow structures. Droplet formation plays an important role in annular flow, and a new droplet entrainment model is proposed, expressed as a phase morphology transfer term from the continuous liquid film to dispersed droplets phase field. The new model is developed based on the shear-off entrainment mechanism on the interfacial wave, implying that the droplet formation is dominated by the balance between the shear forces and the surface tension forces at the gas–liquid interface. In contrast to the existing entrainment models, the new model considers the flow parameters locally at the interface, and it is suitable for phase-resolving CFD frameworks without input of global parameters such as a pipe diameter. The proposed model is implemented in the MultiMorph framework based on the OpenFOAM Foundation release open-source CFD library. The performance of the new model is evaluated by conducting own annular flow experiments with void fraction measurements using electrical resistance tomography, as well as with comparison to published models from the literature. Qualitatively, the model can adequately resolve the formation of interfacial waves on the liquid film downstream from the inlet. The simulated droplets are primarily generated at the tip of such waves, which is consistent with the physical understanding and experimental observations of droplet entrainment. Quantitatively, the modeled entrained droplet fraction matches well the experimental observation in the developing entrainment region. The liquid film fraction obtained with the new model is analyzed and compared with the experimental data. Good agreement between measured and simulated statistics of the liquid film fraction, i.e., the mean, standard deviation, probability density function, and power spectral density, is demonstrated.
Wendelstein 7-X, the world's largest superconducting stellarator in Greifswald (Germany), started plasma experiments with a water-cooled plasma-facing wall in 2022, allowing for long pulse operation. In parallel, a project was launched in 2021 to develop a W based divertor, replacing the current CFC divertor, to demonstrate plasma performance of a stellarator with a reactor relevant plasma facing materials with low tritium retention. The project consists of two tasks: Based on experience from the previous experimental campaigns and improved physics modelling, the geometry of the plasma-facing surface of the divertor and baffles is optimized to prevent overloads and to improve exhaust. In parallel, the manufacturing technology for a W based target module is qualified. This paper gives a status update of project. It focusses on the conceptual design of a W based target module, the manufacturing technology and its qualification, which is conducted in the framework of the EUROfusion funded WPDIV program. A flat tile design in which a target module is made of a single target element is pursued. The technology must allow for moderate curvatures of the plasma-facing surface to follow the magnetic field lines. The target element is designed for steady state heat loads of 10 MW/m2 (as for the CFC divertor). Target modules of a similar size and weight as for the CFC divertor are assumed (approx. <0.25 m2 and <60 kg) using the existing water cooling infrastructure providing 5 l/s and roughly maximum 15 bar pressure drop per module. The main technology under qualification is based on a CuCrZr heat sink made either by additive manufacturing using laser powder bed fusion (LPBF) or by uniaxial diffusion welding of pre-machined forged CuCrZr plates. After heat treatment, the plasma-facing side of the heat sink is covered by W or if feasible by the more ductile WNiFe, preferably by coating or alternatively by hot isostatic pressing W based tiles with a soft OFE-Cu interlayer. Last step is a final machining of the plasma-exposed surface and the interfaces to the water supply lines and supports to correct manufacturing deformations.
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